Following a large earthquake, numerous aftershocks can be triggered due to the complex stress interaction between and within tectonic plates. Although aftershocks are normally smaller in magnitude, their ground motion intensity can be large and have different energy contents than the mainshock. Even seemingly, undamaged buildings may be damaged as a result of aftershocks. The mainshock-damaged buildings with deteriorated structural properties are more susceptible to damage. Based on the achievements of structural engineering and earthquake today, design of structures based on performance can be mentioned. Firstly, unlike traditional methods, new structures can be designed based on seismic needs and functional levels; secondly, the possibility of retrofitting existing buildings is provided. There are also famous ATC and FEMA regulations in this field. In this research, the performance of steel structure with eccentric braced FRAMEs being affected by sequence earthquakes has been studied. To do so, low-rise buildings of 3, 5, and 7 stories have been analyzed in terms of time history dynamics by nonlinear software of Perform 3D. By drawing the fragility curve of structures at different levels of performance, the seismic vulnerability of structures has been investigated. The results indicate that as the number of stories increases, the seismic vulnerability of the structure decreases, and the probability of failure in Far-field earthquakes is higher than near-fault earthquakes. In a seismic sequence discussion, the second earthquake is often affected by the fact that its PGA is larger than the first earthquake. In other words, when the PGA is the second earthquake smaller than or equal to the first earthquake, its effect on structures is very slight, which can be ignored. With regard to the fragility curves achieved, it can be concluded that the structure at the level of the safety of life (LS), which is the standard 2800 and the topic of the tenth subject of the national building regulations, has a good performance, and the design based on them is reliable.